Alternating electrical currents can be measured inductively via the oscillating magnetic fields they generate. FIG. 1 illustrates, as an example, the magnetic field of a straight current-carrying wire 100, which is characterized by circular magnetic field lines 102 in a plane perpendicular to the wire 100. If the magnetic field strength varies due to variations in the underlying current, it can be measured with an induction coil 104 surrounding the field lines 102. In general, however, magnetic sensors are sensitive not only to the magnetic field of the wire of interest (hereinafter referred to as the “primary conductor”), but also to local interfering magnetic fields, which may result in incorrect current readings. Moreover, many traditional induction-based current sensors, such as, e.g., iron core transformers, suffer from rigidity and/or bulkiness that can hinder their installation in crowded spaces, and thus pose practical limits on their use for various applications.
Rogowski coil sensors can overcome many of the problems associated with other current-sensing technologies. FIG. 1 shows the basic structure of a typical Rogowski coil sensor 110 and illustrates its operating principle. The sensor 110 includes a measurement head comprising a helical coil 112 wound around a typically non-ferrous core (e.g., in the simplest case, air), with a return path 114 routed from the end 116 of the coil back to the beginning 118. The end where the coil 112 turns into the return path 114 is commonly referred to as the “free end” of the measurement head or sensor; the other end, where the beginning 118 of the coil 112 and the end of the return path 114 are located, is called the “terminated end.” The measurement head is bent into a substantially closed path (or “loop”) around the primary conductor 100. (The term “substantially closed,” as used herein, allows for a small gap or overlap between the free and terminal ends of the measurement head, which generally cannot be completely avoided in practice, but which do not affect measurements to a level greater than 5%.) To facilitate easy use and re-use of the sensor 110, and to avoid the need to disconnect the conductor to facilitate sensor placement, the measurement head may be sufficiently flexible to allow the loop to be opened and closed repeatedly.
Variations in the magnetic field surrounded by the turns of the coil 112—i.e., the magnetic field of the primary conductor 100—induce a voltage between the terminals 120, 122 of the measurement head (i.e., the beginning of the coil 112 and the end of the return wire 114). The return path 114 serves to subtract out any additional voltages that might be induced between the ends 116, 118 of the coil 112 due to magnetic fields 130 encircled by the coil loop. Thus, the measurement head allows currents to be measured in the primary conductor 100 while rejecting unwanted signals from interfering magnetic fields. Typically, the return path 114 runs along a center axis of the coil 112. However, alternative arrangements, such as a return coil wound on top of the first layer of coil turns, may also be used. To improve measurement accuracy, most Rogowski coil sensors 110 further include an integrator circuit 124 connected between the terminals 120, 122 of the measurement head. The integrator circuit 124 integrates the induced voltage over time, thereby restoring the original waveform of the measured alternating current.
To provide accurate current readings, the Rogowski coil sensor 110 preferably has a coil 112 of uniform cross-section and constant turn density, i.e., uniform spacing between adjacent turns. However, non-uniformities typically arise in the closure region of the coil loop, due to either a gap or an overlap between the free end and the terminated end. While compensatory electronics can, in principle, reduce the impact of these non-uniformities, it increases the cost of the sensor and requires each sensor to be individually calibrated and tuned. Thus, commercially available sensors generally suffer from a trade-off between measurement accuracy and price. The problem is exacerbated in portable measurement applications, where the sensor may need to be re-tuned after each installation around a new conductor (which is not necessary if the sensor is mounted permanently around one primary conductor). A need exists, therefore, for low-cost, flexible, and portable Rogowski coil sensors that reliably provide accurate current measurements for different conductors.